Chapter 10.8, Problem 17P

To determine

To show: The Laplace’s equation in spherical coordinate is $u_{\rho \rho }+\frac{2}{\rho }{u}_{\rho }+\frac{1}{r^2}{u}_{\theta \theta }+\frac{1}{{\rho }^2{\sin }^2\varphi }{u}_{\theta \theta }+\frac{\cot \varphi }{r^2}{u}_{\varphi }=0$.